Cube Root of 64

Cube Root of 64 is 4. Cube Root is a number when multiplied by itself twice (raised to the power of three) gives the original number. The cube root of an integer “x,” which is represented by the symbol ∛x. This is the opposite of cubing a number. For instance, since 2³ (2 raised to the power of 3) equals 8 this implies the cube root of 8 is 2.

In this article, we will learn what is cube root of 64 and the different ways to find the cube root of 64.

What is Cube Root of 64?

Cube Root of 64 is a value obtained when 64 is raised to power 1/3. Cube Root of 64 is 4. It means when 4 is multiplied by 4 twice then the answer is 64. We can express this product as 4 × 4 × 4 = 64. The cube root of 64 can be expressed in following ways:

• Radical Form: ∛64 = 4
• Fractional Exponent Form: (64)^1/3 = 4

Thus, 64 results from raising 4 to the power of 3 i.e. 4³

Cube Root of 64 Calculator

Try out the following cube root calculator to find the cube root of 64

Value of Cube Root of 64

The value of cube root of 64 is mentioned below:

∛64 = 4

How to Find Cube Root of 64

To find the cube root of 64 we can use the following methods:

• Prime Factorization Method
• Long Division Method

Let’s study these methods in detail below:

Cube Root of 64 by Prime Factorization

Use prime factorization to determine the cube root of 64 by doing the following steps:

Step 1: Find the Prime Factorization of the Number 64 which is given as 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

Step 2: Make a group of three like numbers. Hence there will be two groups containing three 2 in each group

Step 3: Now ∛64 = ∛(2³ × 2³). From law of expoents (2³ × 2³)1/3 = 2 × 2 = 4. We can also say that for each three similar prime numbers take out one out of the cube root. Hence, for six twos, there will be two 2s in the form 2 × 2 = 4

Thus the cube root of 64 is 4.

Cube Root of 64 by Long Division Method

To find the cube root by long division method use the following mentioned steps:

Step 1: Make the group of 3 digits. Here, we have 64 that consists of two digits only. Hence will consider these two digits only.

Step 2: Now choose a number whose cube is 64 or nearby and write it in divisor and quotient and add the same number twice in the divisor

Step 3: In this case, divisor and quotient will be 4 as the cube of 4 is 6 and also add 4 twice in the divsior. Hence, the sum is 12 and now if we have a larger number we could be placed a new digit to the right of 12 to find the cube root.

Is Cube Root of 64 Rational or Irrational?

The cube root of 64 is equal to 4 i.e. ∛64 = 4 as it equals 4 since 4³ = 64. Now we can represent 4 in the form of p/q where p and q are integers and q is not equal to 0 i.e. 4/1.

In this case, the denominator is 1 and the numerator is 4. This proves that 64 is a rational number when taken as a cube root.

Cube Root of 64 Frequently Asked Questions

What is Value of Cube Root of 64?

The cube root of 64 is 4 because 4 multiplied by itself twice 4³ equals 64.

Is the Cube Root of 64 a Rational Number?

Yes, the cube root of 64 is a rational number because it can be expressed as the fraction 4/1.

How to Calculate Cube Root of 64?

Cube Root of 64 can be calculated using Prime Factorization or long division method

Is 64 a Perfect Cube?

Yes, 64 is a perfect cube as its cube root is an integer

Is -4 a Cube Root of 64?

No, -4 is not a cube root of 64 as the cube of -4 is -64.